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My self-introduction - Pentalogue - 06/10/2025
My apologize, I wrote my self-introduction here because there is no option to do so in the Community.
Introduction 2025.06.10
Hello people! I'm Pentalogue
My birthday: October 11th
Gender: Male
Pronouns: He/Him/His
I born and live in Russia
Fact:
I'm a lover of electronic music (techno, EDM, trance, house, dubstep, d&b, "growling", ambient), jazz, symphonic, classical music and all sorts of quirky and testing sounds. I study music theory, sound theory and sound processing techniques. I am an budding music and MIDIs creator. As of late, I am now also a fan of normal and black MIDIs.
I also enjoy mathematics, studying number theory, mathematical functions, including those rarely mentioned in maths. I am interested in googology, I like big numbers. I'm into creating graphs on the Desmos website.
I joined this community quite recently and want to understand everything that is happening here and what answers users give to questions regarding the main topic of this forum. As I have noticed, it is quite quiet (deserted) here, and no one has been discussing this complex topic for quite some time.
RE: My self-introduction - MphLee - 08/16/2025
Welcome Pentalogue. I feel math and music are somewhat intimate fields, historically and conceptually.
If you want to understand EVERYTHING here then the best thing to do is to start from the Tetration FAQ and the wikipedia article on tetration.
After that there has been some progress with Trapmann and Kouznetsov theory of complex valued superfunctions, back in the days, and later, we discussed in details James Nixons's serie of papers about the application of his theory of infinite iterated composition and composition integrals to the problem of holomoprhic tetration and holomorphic (in the rank) hyperoperations.
Even more recently the user Natsugou made interesting contribution in the field of negative ranks hyperoperations by an interesting analysis of the algebraic phenomena behind recursion.
Feel free to ask more focused question creating new threads or writing on existing ones.
RE: My self-introduction - Pentalogue - 08/17/2025
Hello, dear MphLee
Yes, I have a lot of questions that I want to ask.
Just in case, I already looked up tetration in both the FAQ and Wikipedia. I also learned about tetration methods, one of which belongs to Kuznetsov and Trappmann. I also found the cross-track method from William Paulsen and Samuel Cowgill's papers, which is based on the Cauchy integral.
I have a task: I need to implement in practice the cross-track method for tetration in the Desmos graphic calculator, since it is one of the most convenient to use.
I need to understand how the Schroöder function and its inverse are implemented, and I also want to understand the formula by which the coefficients of the conformal mapping are calculated.
I look forward to hearing from you.
RE: My self-introduction - MphLee - 08/26/2025
(08/17/2025, 01:59 AM)Pentalogue Wrote: Hello, dear MphLeeHi, good to know you have many questions. The best way to go is, in my opinion, to make a new thread in the "computation" section.
Yes, I have a lot of questions that I want to ask.
Just in case, I already looked up tetration in both the FAQ and Wikipedia. I also learned about tetration methods, one of which belongs to Kuznetsov and Trappmann. I also found the cross-track method from William Paulsen and Samuel Cowgill's papers, which is based on the Cauchy integral.
I have a task: I need to implement in practice the cross-track method for tetration in the Desmos graphic calculator, since it is one of the most convenient to use.
I need to understand how the Schroöder function and its inverse are implemented, and I also want to understand the formula by which the coefficients of the conformal mapping are calculated.
I look forward to hearing from you.
Another good idea is to try your question, perhaps a more specific version of it, on the Q&A site MathSE. I'm sorry I can't redirect you regarding coefficients computation, but I'm sure there are kilometers of posts in this forum that address that problem.